202 Mr. R. Mallet on the Origin and Mechanism of 



similar points taken all round the prism (which, as we shall see 

 hereafter, it will be sufficiently exact to consider as a cylinder), 

 the locus of the resultant through all these points will be in a 

 cone ly i fig. 6. In a homogeneous body the plane of a frac- 

 ture when produced by contractile forces is perpendicular at 

 every point to these forces. The first portion of the fracture 

 through the exterior couche through any point as, o, will not be 

 directly transverse to the axis of the prism> but in a plane normal 

 at that point to or; and taking successive points round the 

 entire circumference, the plane of fracture between /and /' will 

 approximate to a cone whose vertical angle will be Izm. 



Proceeding now to the next isothermal couche within, we may 

 apply the same reasoning to find the direction in which the 

 fracture will proceed through it. If o' be the point at which the 

 fracture through the outside couche is prolonged into the second, 

 then o'p 1 will be the vertical component and very nearly the 

 same as in the former case ; but the horizontal component o f q' is 

 less than for the outside couche by the assumed thickness of that 

 couche, the resultant or rending pull oV is therefore less inclined 

 for this, the second, than for the previous or outside couche, and 

 the fracture through the thickness of the second couche normal 

 to o' r 1 is more nearly transverse to the axis of the prism than, 

 that of the outside couche ; and so on for every successive couche 

 until we arrive at the axis of the prism, where the plane of the 

 fracture will be exactly transverse to it. Assuming the succes- 

 sive couches of indefinitely small thickness, the entire fracture 

 through the prism will be thus in the form of a lens at the con- 

 vex side, or of a corresponding shallow cup at the concave side — 

 the convex side of the curve of fracture always presenting itself 

 in the direction opposite to that in which the cooling of the 

 prism is occurring, or towards the hotter part of the prism. 



Referring now to fig. 7 (which represents an axial section 

 below the first cross joint, already referred to, and between'that 

 and the second joint), it will be obvious that the curvature of the 

 cup-shaped fracture will slightly differ from that of the first 

 joint as in fig. 6. For at the point o, corresponding to that in 

 fig. 6, the vertical component op is the same as in fig. 6, and 

 so is o q, and the angle of the resultant o r is also the same ; 

 therefore the angle of the plane of fracture at the surface of the 

 prism is the same as in fig. 6 ; but as the top surface of the 

 whole mass of basalt, assumed as a horizontal plane S S in fig. 6 

 is the origin of all the vertical components down to the first 

 joint, so these increase slightly in succession as they approach 

 the axis : but after the first fracture has been effected, the 

 origin of the vertical components producing the second and all 

 subsequent joints is to be found in the hollow surface of the pre*- 



